On the Fréchet Differentiability of Invariant Tori of Countable Systems of Difference Equations Defined on Infinite-Dimensional Tori

Abstract

By using the method of Green–Samoilenko functions, in the space of bounded number sequences we construct invariant tori of linear and nonlinear systems of discrete equations defined on infinite-dimensional tori. We establish sufficient conditions for the Fréchet differentiability of invariant tori.